Abstract
In modular representation theory of finite groups there has been a well-known conjecture due to P. Donovan. Donovan conjecture is on blocks of group algebras of finite groups over an algebraically closed field k of prime characteristic p, which says that, for any given finite p-group P, up to Morita equivalence, there are only finitely many block algebras with defect group P. We prove that Donovan conjecture holds for principal block algebras in the case where P is elementary abelian 3-group of order 9. Moreover, under the same assumption, namely, if G is a finite group with elementary abelian Sylow 3-subgroup P of order 9, then the Loewy length of the principal block algebra B 0 (kG) of the group algebra kG is 5 or 7. The results here depend on the classification of finite simple groups.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.